Measuring star formation rates (SFRs) in high-z galaxies with their rest-frame ultraviolet (UV) continuum can be uncertain because of dust obscuration. Prior studies had used the submillimeter emission at 850 um to determine the intrinsic SFRs of rest-frame UV selected galaxies, but the results suffered from the low sensitivity and poor resolution (~15''). Here, we use ultradeep Very Large Array 1.4 GHz images with ~1''-2'' resolutions to measure the intrinsic SFRs. We perform stacking analyses in the radio images centered on ~3500 Lyman break galaxies (LBGs) at z~4 in the Great Observatories Origins Deep Survey-North and South fields selected with Hubble Space Telescope/Advanced Camera for Surveys data. The stacked radio flux is very low, 0.08+/-0.15 uJy, implying a mean SFR of 6+/-11 M/yr. This is comparable to the uncorrected mean UV SFRs of 5 M/yr, implying that the z~4 LBGs have little dust extinction. The low SFR and dust extinction support the previous results that z~4 LBGs are in general not submillimeter galaxies. We further show that there is no statistically significant excess of dust-hidden star-forming components within ~22 kpc from the LBGs.